Finite Group Databasebeta

← #11864218

Subgroups — #11864218

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×#64118C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic, complemented
8#10590970C212yesmaximal, complemented
9#10590969C212yesmaximal, complemented
10#10590952C212yesmaximal, complemented
11#10590946C212yesmaximal, complemented
12#78885—31nomaximal
13#78640—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×#634C2211yescharacteristic, complemented
16C2×C3×#235C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×D3×#67—21no—
19C2×#3804—21no—
20D3×#235—24no—
21D3×#235—24no—
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32—21no—
24C2×#3799C2211yescharacteristic
25C2×#3798—21no—
26C2×#3795C2211yescharacteristic
27C2×D3×Dic6C2211yescharacteristic
28C2×C32×M16C2211yescharacteristic, complemented
29#64118—24no—
30C2×#3746C2212yescomplemented
31C2×#3744C2212yescomplemented
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×#208C2211yescharacteristic, complemented
34C2×Dic3⋊Dic3—21no—
35C2×(C2×D3)⋊Dic3—21no—
36#63857—21no—
37#63857—21no—
38#63857C2212yes—
39#63857C2212yescomplemented
40C2×#3719C2212yescomplemented
41#63831—24no—
42C2×#3716C2212yescomplemented
43C3×#821C2212yescomplemented
44C3×(C2×D3)⋊C8C2212yes—
45C3×(C2×D3)⋊C8C2212yescomplemented
46C3×#816C2212yescomplemented
47#63567C2212yescomplemented
48#63564C2212yescomplemented
49C2×D3×#41—31no—
50C22×#235—31no—
51C2×#951—31no—
52C2×#924—31no—
53C2×#909—31no—
54C2×#909—31no—
55C2×#909—31no—
56C2×#909—61no—
57C2×#897—31no—
58C3×#417—31no—
59C3×#407—31no—
60#5133—31no—
61#5133D311yescharacteristic, complemented
62#5126D311yescharacteristic, complemented
63#4966—31no—
64#4809—32no—
65#4808—32no—
66#4783—32no—
67#4776—32no—
68#4739—32no—
69#4733—32no—
70#4733—32no—
71#4731—32no—
72C23×C3×D3D411yescharacteristic
73C22×D32—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76C22×C3⋊Dic3—21no—
77#3828—22no—
78#3828D414yes—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4×C3⋊D3—21no—
81C2×#634—22no—
82C2×#634—22no—
83C2×#634—21no—
84C2×#634C2312yes—
85C2×#634C2311yescharacteristic
86C2×C3×#67—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3D411yescharacteristic
89C3×#235—22no—
90C3×#235D414yes—
91C2×C3×D12C2311yescharacteristic
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—22no—
95C2×C3×C4×D3D411yescharacteristic
96C2×C3×C4×D3D411yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100D3×#67—28no—
101C2×#627—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106#3804—28no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C4×D32—28no—
112#3799—22no—
113#3799—22no—
114#3798—28no—
115#3795—22no—
116#3795—22no—
117D3×Dic6—22no—
118D3×Dic6—22no—
119C32×M16—22no—
120C2×C32×C8C2312yes—
121#3746—24no—
122#3744—24no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2312yes—
125C3×#208—22no—
126C2×C3×C3⋊C8C2312yes—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131#3719—24no—
132#3716—24no—
133#3007—91noSylow
134C2×C3×#41—31no—
135C23×C3×C4—31no—
136C22×#67—61no—
137D3×#41—64no—
138D3×#41—64no—
139C2×#239—31no—
140C2×D3×Q8—31no—
141C2×#237—31no—
142C2×#237—61no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×#235—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—61no—
150C2×#235—61no—
151C2×#235—64no—
152C2×#235—61no—
153C2×#235—64no—
154C2×#235—61no—
155C2×#235C2×D311yescharacteristic
156C22×D12—31no—
157C22×C4×D3—61no—
158C22×C4×D3—61no—
159C22×C4×D3C2×D311yescharacteristic
160C22×Dic6—31no—
161C22×Dic6—31no—
162C22×Dic6—31no—
163C22×Dic6—61no—
164C2×C3×M16—21no—
165C2×C3×M16—31no—
166C2×C3×M16C2×D311yescharacteristic, complemented
167C2×C3×M16C2×D311yescharacteristic, complemented
168C2×C3×C4⋊C4—31no—
169C2×#217—61no—
170#951—64no—
171C2×#216—32no—
172C2×#214—32no—
173C2×(C2×D3)⋊C4—61no—
174C2×C4⋊Dic3—61no—
175C2×C4⋊Dic3C2×D311yescharacteristic, complemented
176#924—32no—
177#924—32no—
178#924—61no—
179#924—61no—
180C2×Dic3⋊C4—61no—
181C2×#208C2×D311yescharacteristic, complemented
182#909—64no—
183#909—64no—
184#909—68no—
185#909—64no—
186C2×Dic12—32no—
187C2×Dic12—32no—
188C2×Dic12—32no—
189C2×Dic12—62no—
190C2×#204—32no—
191C2×#204—32no—
192C2×#204—32no—
193C2×#204—62no—
194#897—32no—
195#897—32no—
196#897—61no—
197#897—61no—
198C3×#103—32no—
199C3×#102—32no—
200C3×C22⋊C8—32no—
201C3×C22⋊C8—32no—
202#821—32no—
203#821C2×D312yescomplemented
204(C2×D3)⋊C8C2×D312yes—
205(C2×D3)⋊C8C2×D312yescomplemented
206#816—32no—
207#816C2×D312yescomplemented
208#810—32no—
209#809—32no—
210C23×C32C2×D411yescharacteristic
211C22×C3⋊D3—21no—
212C22×C3×D3—22no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—41no—
216C22×C3×D3C2×D411yescharacteristic
217C22×C3×D3C2×D411yescharacteristic
218C2×D32—24no—
219C2×D32—42no—
220C2×D32—42no—
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2×D412yes—
223C2×C32×C4C2×D412yes—
224C2×C32×C4C2411yescharacteristic
225#638—24no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—22no—
228C2×C3⋊Dic3—42no—
229C4⋊(C3⋊D3)—21no—
230C4⋊(C3⋊D3)C2×D412yes—
231C4×C3⋊D3—24no—
232#634—22no—
233#634—21no—
234#634—22no—
235#634—42no—
236#634C2×D412yes—
237C3×#67—24no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—42no—
242C2×C3×Dic3C2×D411yescharacteristic
243C2×C3×Dic3C2×D411yescharacteristic
244C3×D12—21no—
245C3×D12C2×D412yes—
246C3×C4×D3—22no—
247C3×C4×D3—24no—
248C3×C4×D3—22no—
249C3×C4×D3—21no—
250C3×C4×D3—21no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×Dic6—21no—
254C3×Dic6C2×D412yes—
255#627—24no—
256#626—24no—
257#626—24no—
258#625—24no—
259#624—24no—
260D3×Dic3—24no—
261D3×Dic3—24no—
262C32×C8—22no—
263C3×C3⋊C8—22no—
264C22×#41—91no—
265C2×#137—91no—
266C2×#137—91no—
267C2×C22⋊Q8—91no—
268#452—92no—
269#452—92no—
270#451—92no—
271#450—92no—
272#417—31no—
273#417—91no—
274#407—31no—
275C24×C3—31no—
276C23×D3—61no—
277C23×D3—61no—
278C23×D3D1211yescharacteristic
279C3×#41—34no—
280C3×#41—62no—
281C2×C3×Q8—31no—
282C2×C3×D4—31no—
283C2×C3×D4—61no—
284C22×C3×C4—21no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—61no—
291C22×C3×C4—62no—
292C22×C3×C4—62no—
293C22×C3×C4—61no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C2×#67—21no—
297C2×#67—61no—
298C2×#67—68no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—121no—
305C22×Dic3—21no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—121no—
311C22×Dic3D1211yescharacteristic
312#239—62no—
313#239—62no—
314D3×Q8—62no—
315D3×Q8—62no—
316#237—62no—
317#237—62no—
318#237—68no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—68no—
322#235—22no—
323#235—34no—
324#235—34no—
325#235—64no—
326#235—62no—
327#235—62no—
328#235—68no—
329#235—68no—
330#235—68no—
331#235—62no—
332#235—62no—
333#235—62no—
334#235—62no—
335#235—122no—
336#235D1214yes—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—62no—
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—21no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—68no—
349C2×C4×D3—68no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—121no—
357C2×C4×D3D1211yescharacteristic
358C2×C4×D3D1211yescharacteristic
359C2×C4×D3C22×D311yescharacteristic
360C2×C4×D3C22×D311yescharacteristic
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—32no—
364C2×Dic6—32no—
365C2×Dic6—62no—
366C2×Dic6—61no—
367C2×Dic6—62no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—62no—
371C2×Dic6—64no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6—121no—
379C2×Dic6—122no—
380C2×Dic6C22×D311yescharacteristic
381C3×M16—24no—
382C3×M16—22no—
383C3×M16—22no—
384C3×M16—62no—
385C2×C3×C8—22no—
386C2×C3×C8—32no—
387C2×C3×C8C22×D312yes—
388C2×C3×C8C22×D312yes—
389C3×C4⋊C4—32no—
390C3×C4⋊C4—61no—
391#217—62no—
392#217—62no—
393#216—64no—
394#214—64no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397C4⋊Dic3—21no—
398C4⋊Dic3—62no—
399C4⋊Dic3—62no—
400C4⋊Dic3C22×D312yes—
401Dic3⋊C4—62no—
402Dic3⋊C4—62no—
403#208—22no—
404C2×C3⋊C8C22×D312yes—
405Dic12—64no—
406Dic12—64no—
407Dic12—68no—
408Dic12—64no—
409#204—64no—
410#204—64no—
411#204—68no—
412#204—64no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32#12012yes—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—44no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3#13712yescomplemented
430D32—48no—
431C32×C4#12012yes—
432C32×C4C22×D411yescharacteristic
433C32×C4C22×D411yescharacteristic
434C3⋊Dic3—22no—
435C3⋊Dic3—42no—
436C3×Dic3—21no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—42no—
440C2×#41—31no—
441C2×#41—91no—
442C2×#41—91no—
443C2×#41—91no—
444C2×#41—181no—
445C2×#41—181no—
446C2×#41—184no—
447C2×#41—184no—
448C22×Q8—91no—
449C22×Q8—91no—
450C22×D4—91no—
451C22×D4—181no—
452C23×C4—31no—
453C23×C4—181no—
454#137—184no—
455#137—184no—
456C2×Q16—92no—
457C2×Q16—92no—
458C2×SD16—92no—
459C2×SD16—92no—
460C2×M16—31no—
461C2×M16D3211yescharacteristic, complemented
462C22⋊Q8—92no—
463C22⋊Q8—92no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—181no—
468C2×C22⋊C4—181no—
469#103—32no—
470#103—92no—
471#102—32no—
472#102—92no—
473C22⋊C8—32no—
474C22⋊C8—32no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3—31no—
478C23×C3—62no—
479C23×C3—62no—
480C23×C3—61no—
481C23×C3—121no—
482C23×C3C2×D1211yescharacteristic
483C23×C3D3×D411yescharacteristic
484C22×D3—22no—
485C22×D3—21no—
486C22×D3—22no—
487C22×D3—41no—
488C22×D3—64no—
489C22×D3—64no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3C2×D1211yescharacteristic
498C22×D3C2×D1211yescharacteristic
499C3×Q8—32no—
500C3×Q8—61no—
501C3×D4—32no—
502C3×D4—64no—
503C3×D4—61no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—62no—
511C2×C3×C4—61no—
512C2×C3×C4—62no—
513C2×C3×C4—64no—
514C2×C3×C4—62no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—62no—
520C2×C3×C4—122no—
521C2×C3×C4C2×D1211yescharacteristic
522C2×C3×C4C2×D1212yes—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D412yes—
525C2×C3×C4D3×D412yes—
526C2×C3×C4D3×D412yes—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530#67—64no—
531#67—64no—
532#67—64no—
533#67—64no—
534#67—64no—
535#67—64no—
536#67—124no—
537C2×Dic3—22no—
538C2×Dic3—21no—
539C2×Dic3—22no—
540C2×Dic3—42no—
541C2×Dic3—64no—
542C2×Dic3—64no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—122no—
548C2×Dic3—121no—
549C2×Dic3—124no—
550C2×Dic3—122no—
551C2×Dic3—122no—
552C2×Dic3C2×D1211yescharacteristic
553C2×Dic3C2×D1211yescharacteristic
554D12—21no—
555D12—32no—
556D12—32no—
557D12—62no—
558D12—64no—
559D12—64no—
560D12—61no—
561D12—61no—
562D12—121no—
563D12C2×D1212yes—
564C4×D3—22no—
565C4×D3—22no—
566C4×D3—24no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—64no—
572C4×D3—64no—
573C4×D3—64no—
574C4×D3—64no—
575C4×D3—64no—
576C4×D3—64no—
577C4×D3—124no—
578Dic6—21no—
579Dic6—32no—
580Dic6—32no—
581Dic6—62no—
582Dic6—64no—
583Dic6—64no—
584Dic6—61no—
585Dic6—61no—
586Dic6—64no—
587Dic6—62no—
588Dic6—62no—
589Dic6—62no—
590Dic6—62no—
591Dic6—122no—
592Dic6—121no—
593Dic6—124no—
594Dic6—122no—
595Dic6—122no—
596Dic6C2×D1212yes—
597C3×C8—24no—
598C3×C8—22no—
599C3×C8—22no—
600C3×C8—62no—
601C3⋊C8—22no—
602C2×C32—22no—
603C2×C32C2×#12011yescharacteristic
604C2×C32C2×#13711yescharacteristic
605C2×C32#57511yescharacteristic
606C3⋊D3—42no—
607C3×D3—22no—
608C3×D3—42no—
609C3×D3—41no—
610C24—31no—
611C24—181no—
612#41—34no—
613#41—62no—
614#41—94no—
615#41—188no—
616#41—182no—
617#41—182no—
618#41—188no—
619#41—182no—
620#41—182no—
621#41—182no—
622C2×Q8—31no—
623C2×Q8—91no—
624C2×Q8—92no—
625C2×Q8—181no—
626C2×Q8—182no—
627C2×Q8—182no—
628C2×Q8—181no—
629C2×Q8—182no—
630C2×Q8—182no—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—91no—
634C2×D4—181no—
635C2×D4—182no—
636C2×D4—182no—
637C2×D4—181no—
638C2×D4—188no—
639C2×D4—181no—
640C2×D4—181no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—62no—
647C22×C4—61no—
648C22×C4—62no—
649C22×C4—61no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4—188no—
653C22×C4—181no—
654C22×C4—181no—
655C22×C4—181no—
656C22×C4C2×D3211yescharacteristic
657Q16—184no—
658Q16—184no—
659SD16—184no—
660SD16—184no—
661M16—22no—
662M16—62no—
663C2×C8—32no—
664C2×C8C2×D3212yes—
665C4⋊C4—32no—
666C4⋊C4—61no—
667C4⋊C4—182no—
668C4⋊C4—182no—
669C22⋊C4—182no—
670C22⋊C4—182no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—22no—
677C22×C3—32no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—62no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—124no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3#88212yes—
690C22×C3#88212yes—
691C22×C3C22×D1211yescharacteristic
692C22×C3C2×D3×D411yescharacteristic
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—22no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—44no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—62no—
703C2×D3—62no—
704C2×D3—122no—
705C2×D3—128no—
706C2×D3—128no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3#90912yescomplemented
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—22no—
717C3×C4—61no—
718C3×C4—62no—
719C3×C4—61no—
720C3×C4—122no—
721C3×C4#88212yes—
722C3×C4#88212yes—
723C3×C4C22×D1211yescharacteristic
724C3×C4C2×D3×D411yescharacteristic
725C3×C4C2×D3×D411yescharacteristic
726C3×C4C2×D3×D411yescharacteristic
727Dic3—22no—
728Dic3—21no—
729Dic3—21no—
730Dic3—42no—
731Dic3—62no—
732Dic3—62no—
733Dic3—122no—
734Dic3—124no—
735Dic3—122no—
736Dic3—122no—
737C32#300711yescharacteristic, complemented, Sylow
738C23—31no—
739C23—31no—
740C23—62no—
741C23—61no—
742C23—62no—
743C23—121no—
744C23—184no—
745C23—181no—
746C23—362no—
747C23—362no—
748C23D3×D1211yescharacteristic
749Q8—32no—
750Q8—61no—
751Q8—92no—
752Q8—184no—
753Q8—181no—
754Q8—182no—
755Q8—182no—
756Q8—362no—
757D4—32no—
758D4—64no—
759D4—61no—
760D4—92no—
761D4—184no—
762D4—184no—
763D4—184no—
764D4—184no—
765D4—181no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—61no—
769C2×C4—62no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—64no—
777C2×C4—62no—
778C2×C4—122no—
779C2×C4—184no—
780C2×C4—184no—
781C2×C4—184no—
782C2×C4—181no—
783C2×C4—184no—
784C2×C4—182no—
785C2×C4—362no—
786C2×C4D3×D1212yes—
787C2×C4D3×D1211yescharacteristic
788C2×C4#381112yes—
789C2×C4C22×D3211yescharacteristic
790C8—22no—
791C8—62no—
792C2×C3—22no—
793C2×C3—22no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—62no—
799C2×C3—121no—
800C2×C3—122no—
801C2×C3C2×#88211yescharacteristic
802C2×C3C2×#88211yescharacteristic
803C2×C3C2×#90911yescharacteristic
804C2×C3#574811yescharacteristic
805C2×C3#577311yescharacteristic
806C2×C3D3×#13711yescharacteristic
807D3—22no—
808D3—42no—
809D3—41no—
810D3—122no—
811D3—122no—
812D3—242no—
813C22—21no—
814C22—21no—
815C22—32no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—61no—
821C22—62no—
822C22—124no—
823C22—121no—
824C22—121no—
825C22—182no—
826C22—368no—
827C22—361no—
828C22—361no—
829C22#6392312yes—
830C22C2×D3×D1211yescharacteristic
831C4—61no—
832C4—61no—
833C4—62no—
834C4—122no—
835C4—182no—
836C4—362no—
837C4#6392312yes—
838C4C2×D3×D1211yescharacteristic
839C4C2×#381111yescharacteristic
840C3—21no—
841C3#7864011yescharacteristic, complemented
842C3#7888511yescharacteristic, complemented
843C2—22no—
844C2—62no—
845C2—121no—
846C2—122no—
847C2—362no—
848C2D3×#90911yescharacteristic
849C2#1059471211yescharacteristic
850C2C2×#6392311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
hypercenterC2×M16D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#64118C2semidirect
3. C2×#63857C2semidirect
4. C2×#63831C2semidirect
5. C3×#5133C2semidirect
6. C3×#5126C2semidirect
7. #10591106C2semidirect
8. #10590970C2semidirect
9. #10590969C2semidirect
10. #10590952C2semidirect
11. #10590946C2semidirect
15. C22×#634C22semidirect
28. C2×C32×M16C22semidirect
30. C2×#3746C22semidirect
31. C2×#3744C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×#208C22semidirect
39. #63857C22semidirect
40. C2×#3719C22semidirect
42. C2×#3716C22semidirect
43. C3×#821C22semidirect
45. C3×(C2×D3)⋊C8C22semidirect
46. C3×#816C22semidirect
47. #63567C22semidirect
48. #63564C22semidirect
61. #5133D3semidirect
62. #5126D3semidirect
166. C2×C3×M16C2×D3semidirect
167. C2×C3×M16C2×D3semidirect
175. C2×C4⋊Dic3C2×D3semidirect
181. C2×#208C2×D3semidirect
203. #821C2×D3semidirect
205. (C2×D3)⋊C8C2×D3semidirect
207. #816C2×D3semidirect
429. C2×C3×D3#137semidirect
461. C2×M16D32semidirect
713. C2×D3#909semidirect
737. C32#3007semidirect
841. C3#78640semidirect
842. C3#78885semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D3×#2352
C2×#641182
C2×#638572
C2×#638312
C3×#51332
C3×#51262
#105911062
#105909702
#105909692
#105909522
#105909462
#788853
#786403